System and Methods for Finding Hidden Topics of Documents and Preference Ranking Documents

1. A computer-implemented method to apply a query to a set of documents, comprising: by a computer: reconstructing a document term matrix XεR N×M where N is a number of documents and M is a number of words, by minimizing reconstruction errors with min ∥X−UA∥, where A is a fixed projection matrix and U is a column orthogonal matrix; determining a loss function and parameter gradients to generate U; fixing U while determining the loss function and sparse regularization constraints on the projection matrix A; generating parameter coefficients and generating a sparse projection matrix A; and generating a Sparse Latent Semantic Analysis (Sparse SLA) model and applying the model to a set of documents and displaying documents matching a query.

2. The computer-implemented method of claim 1 , wherein the document-term matrix comprises XεR N×M , where N is the number of documents and M is the number of words, and where a column orthogonal matrices UεR N×D (U T U=I) and VεR M×D (V T V=I) represent document and word embeddings into a latent space, and where I comprises a unity matrix.

3. The method of claim 1 , comprising automatically selecting most relevant words for each latent topic.

4. The method of claim 1 , comprising projecting documents with the sparse projection matrix.

5. The method of claim 1 , comprising adding an entry-wise l 1 -norm of A as a regularization term to the loss function and formulating the Sparse LSA model as: min U , A ⁢ 1 2 ⁢  X - UA  F 2 + λ ⁢  A  1 subject ⁢ - ⁢ to ⁢ : ⁢ ⁢ U T ⁢ U = I , where  A  1 = ∑ d = 1 D ⁢ ⁢ ∑ j = 1 M ⁢  a dj  is the entry-wise l 1 -norm of A and λ is a regularization parameter for a density (the number of nonzero entries) of A.

6. The method of claim 1 , comprising optimizing A according to the following relationship: min A ⁢ 1 2 ⁢  X - UA  + λ ⁢  A  1 .

7. The method of claim 6 , comprising solving M independent optimizations according to the following relationship: min A j ⁢ 1 2 ⁢  X j - UA j  2 2 + λ ⁢  A j  1 ; j = 1 , … ⁢ , M .

8. The method of claim 1 , comprising initializing U 0 = ( I D 0 ) , where I comprises a unity matrix and D comprises a dimensionality of a latent space.

9. The method of claim 1 , comprising iterating until convergence of U and A .

10. The method of claim 1 , comprising determining A by solving M LASSO problems.

11. The method of claim 10 , comprising determining: min A j ⁢ 1 2 ⁢  X j - UA j  2 2 + λ ⁢  A j  1 ; j = 1 , … ⁢ , M .

12. The method of claim 1 , comprising projecting X onto a latent space V=XA T .

13. The method of claim 1 , comprising generating V:V=PΔQ where U=PQ.

14. The method of claim 1 , comprising: determining A by solving M LASSO problems; projecting X onto a latent space V=XA T ; determining V=PΔQ where U=PQ; and generating the sparse projection matrix A.

15. The method of claim 1 , comprising determining a Group Structured Sparse LSA.

16. The method of claim 15 , comprising using a group structured sparsity-inducing penalty to select most relevant groups of features relevant to a latent topic.

17. The method of claim 1 , comprising enforcing a non-negative constraint on the projection matrix.

18. The method of claim 17 , comprising determining min U , A ⁢ 1 2 ⁢  X - UA  F 2 + λ ⁢  A  1 subject ⁢ ⁢ to ⁢ ⁢ U T ⁢ U = I , ⁢ A ≥ 0.

19. The method of claim 17 , comprising determining min U , A ⁢ 1 2 ⁢  X - UA  F 2 + λ ⁢ ∑ d = 1 D ⁢ ∑ j = 1 J ⁢ a dj subject ⁢ ⁢ to ⁢ ⁢ U T ⁢ U = I , ⁢ A ≥ 0.

20. A system to perform preference learning on a set of documents, comprising a computing device including a processor and a memory coupled to said processor, said memory having stored thereon computer executable instructions that upon execution by the processor cause the system to: receive raw input features from the set of documents stored on a data storage device and generate polynomial combinations from the raw input features; generate one or more parameters; apply the parameters to one or more classifiers to generate outputs; determine a loss function and parameter gradients and updating parameters determining one or more sparse regularizing terms and updating the parameters; and expressing that one document is preferred over another in a search query and retrieving one or more documents responsive to the search query.